Modelling the shrinking generator in terms of linear CA

Sara D.  Cardell; Amparo  Fúster-Sabater

doi:10.3934/amc.2016041

Article Contents

2016, Volume 10, Issue 4: 797-809. Doi: 10.3934/amc.2016041

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Modelling the shrinking generator in terms of linear CA

Sara D. Cardell^1, and
Amparo Fúster-Sabater^2,

1.
Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas (UNICAMP), R. Sérgio Buarque de Holanda, 651, Cidade Universitária, Campinas - SP, 13083-859
2.
Instituto de Tecnologías Físicas y de la Información, Consejo Superior de Investigaciones Científicas, C/Serrano 144, 28006, Madrid

Received: December 2014

Revised: June 2016

Published: November 2016

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Abstract

This work analyses the output sequence from a cryptographic non-linear generator, the so-called shrinking generator. This sequence, known as the shrunken sequence, can be built by interleaving a unique PN-sequence whose characteristic polynomial serves as basis for the shrunken sequence's characteristic polynomial. In addition, the shrunken sequence can be also generated from a linear model based on cellular automata. The cellular automata here proposed generate a family of sequences with the same properties, period and characteristic polynomial, as those of the shrunken sequence. Moreover, such sequences appear several times along the cellular automata shifted a fixed number. The use of discrete logarithms allows the computation of such a number. The linearity of these cellular automata can be advantageously employed to launch a cryptanalysis against the shrinking generator and recover its output sequence.

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Mathematics Subject Classification: Primary: 37B15, 11B85; Secondary: 12E05.

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References

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